Stein approximation for functionals of independent random sequences
Date of Issue2018
School of Physical and Mathematical Sciences
We derive Stein approximation bounds for functionals of uniform random variables, using chaos expansions and the Clark-Ocone representation formula combined with derivation and finite difference operators. This approach covers sums and functionals of both continuous and discrete independent random variables. For random variables admitting a continuous density, it recovers classical distance bounds based on absolute third moments, with better and explicit constants. We also apply this method to multiple stochastic integrals that can be used to represent U-statistics, and include linear and quadratic functionals as particular cases.
Electronic Journal of Probability
© 2018 The Author(s) (published by Bernouli Society and the Institute of Mathematical Statistics). This paper was published in Electronic Journal of Probability and is made available as an electronic reprint (preprint) with permission of Bernouli Society and the Institute of Mathematical Statistics. The published version is available at: [http://dx.doi.org/10.1214/17-EJP132]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.